Isovariant Borsuk-Ulam results for pseudofree circle actions and their converse

Abstract

Abstract. In this paper we shall study the existence of an S 1 -isovariant map from a rational homology sphere M with pseudofree action to a representation sphere SW . We first show some isovariant Borsuk-Ulam type results. Next we shall consider the converse of those results and show that there exists an S 1 -isovariant map from M to SW under suitable conditions.